Uncertainty updating in the description of heterogeneous materials

At a macroscopic scale, the details of mechanical behaviour are often uncertain, due to incomplete knowledge of details at small scales; this is especially acute if the materials have to be described before actually having been manufactured, such as in the case of concrete. Here the uncertainties are described by probabilistic methods, using recent numerical techniques for random fields based on white noise analysis. Numerical procedures are then developed to change/update the description once the materials have been manufactured, in order to take into accountadditionalinformation, obtainedforexamplefrommeasurements. This results in an improved description of the uncertainties of the material behaviour

The use of openfoam as a virtual laboratory to simulate oscillating water column wave energy converters

The Oscillating Water Column is one of the oldest concepts for wave energy harvesting. T e device optimization is still a crucial point for the commercial-scale diffusion of this technology. Therefore, research at fundamental level is still required. The implementation and the application a CFD code for the conduction of a parameter study aiming at the optimization of the device is presented. The numerical set up and the validation of a virtual wave flume in the open-source environment OpenFOAM® are initially presented, using comparatively different wave generation approaches. The application of the model to simulate the device and a validation with physical results are shown. The model solves incompressible 3D Navier-Stokes equations for a single Eulerian fluid mixture of water and air, using a Finite Volume Method for equations discretization and the Volume Of Fluid method for free surface tracking. Different turbulence models are tested, comparing their suitability for this particular application both in terms of computational cost and model capability to reproduce the experimental data

Sparse data formats and efficient numerical methods for uncertainties quantification in numerical aerodynamics

The problem to be considered is the stationar system of Navier-Stokes equations with uncertain parameters and uncertain computational domain. We research how uncertainties in the angle of attack, in the Mach number and in the geometry of the airfoil propagate in the solution. The uncertain solution of this problem (pressure, density, velocity etc) is approximated via random fields. Since the whole set of realisations of these random fields are too much information, we demonstrate an algorithm of their low-rank approximation. This algorithm, working on the fly, is based on the QR-decomposition and has a linear complexity. This low-rank approximation allows us an effective postprocessing (computation of the mean value, variance, exceedance probability) with drastically reduced memory requirements

Probabilistic optimization of engineering system with prescribed target design in a reduced parameter space

A novel probabilistic robust design optimization framework is presented here using a Bayesian inference framework. The objective of the proposed study is to obtain probabilistic descriptors of the system parameters conditioned on the user-prescribed target probability distributions of the output quantities of interest or figures of merit of a system. A criterion-based identification of a reduced important parameter space is performed from the typically high number of parameters modelling the stochastically parametrized physical system. The criterion can be based on sensitivity indices, design constraints or expert opinion or a combination of these. The posterior probabilities on the reduced or important parameters conditioned on prescribed target distributions of the output quantities of interest is derived using the Bayesian inference framework. The probabilistic optimal design proposed here offers the distinct advantage of prescribing probability bounds of the system performance functions around the optimal design points such that robust operation is ensured. The proposed method has been demonstrated with two numerical examples including the optimal design of a structural dynamic system based on user-prescribed target distribution for the resonance frequency of the system

Efficient Analysis of High Dimensional Data in Tensor Formats

In this article we introduce new methods for the analysis of high dimensional data in tensor formats, where the underling data come from the stochastic elliptic boundary value problem. After discretisation of the deterministic operator as well as the presented random fields via KLE and PCE, the obtained high dimensional operator can be approximated via sums of elementary tensors. This tensors representation can be effectively used for computing different values of interest, such as maximum norm, level sets and cumulative distribution function. The basic concept of the data analysis in high dimensions is discussed on tensors represented in the canonical format, however the approach can be easily used in other tensor formats. As an intermediate step we describe efficient iterative algorithms for computing the characteristic and sign functions as well as pointwise inverse in the canonical tensor format. Since during majority of algebraic operations as well as during iteration steps the representation rank grows up, we use lower-rank approximation and inexact recursive iteration schemes

A Worked-out Example of Surrogate-based Bayesian Parameter and Field Identification Methods

none4sinoneFriedman, Noémi; Zoccarato, Claudia; Zander, Elmar; Matthies, Hermann G.Friedman, Noémi; Zoccarato, Claudia; Zander, Elmar; Matthies, Hermann G

Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space